Asymptotes

Algebra 2A Perspective 2008-09

= = Algebra 2C Perspective 2008-09

__ What are Asymptotes? __
Asymptotes are the line(s) that the graph of a function approaches but will never touch.

__ Example 1 __ In the graph below the line approaches the x-axis, but never touches it no matter how far we extend the graph horizontally. You may also notice that the graph approaches the y-axis, but never touches it no matter how far we extend the graph vertically.



__ Example 2 __ In viewing the graph below, you will see that the lines approach the x-axis but never touch it. The x-axis would be a horizontal asymptote. The equation x = 0 can also be used to describe the horizontal asymptote. The lines for the graph below also seem to approach a vertical asymptote.

__ Further Discussion __

 * What is the equation for the vertical asymptote in Example #2?
 * How can we determine if an equation has a vertical or horizontal asymptote without graphing

Sophia Moreno
 * EF-100** (The only asymtote problem I could find from this year)

Graph math f(x) = \frac{5}{X^2 + 1} - 1 math Name intercepts, domain and range



The asymptote is y = -1 The line will approach Y = -1, but never reach it.